100.104 Problem number 4339

\[ \int \frac {e^{e^x} \left (5-10 x+e^x \left (25-5 x+5 x^2\right )-80 x^2 \log ^3\left (x^2\right )+\left (-30 x^2+10 e^x x^3\right ) \log ^4\left (x^2\right )-80 x^3 \log ^7\left (x^2\right )+\left (-20 x^3+5 e^x x^4\right ) \log ^8\left (x^2\right )\right )}{25-10 x+11 x^2-2 x^3+x^4+\left (20 x^3-4 x^4+4 x^5\right ) \log ^4\left (x^2\right )+\left (10 x^4-2 x^5+6 x^6\right ) \log ^8\left (x^2\right )+4 x^7 \log ^{12}\left (x^2\right )+x^8 \log ^{16}\left (x^2\right )} \, dx \]

Optimal antiderivative \[ \frac {{\mathrm e}^{{\mathrm e}^{x}}}{1-\frac {x}{5}+\frac {\left (x +\ln \left (x^{2}\right )^{4} x^{2}\right )^{2}}{5}} \]

command

integrate(((5*exp(x)*x^4-20*x^3)*log(x^2)^8-80*x^3*log(x^2)^7+(10*exp(x)*x^3-30*x^2)*log(x^2)^4-80*x^2*log(x^2)^3+(5*x^2-5*x+25)*exp(x)-10*x+5)*exp(exp(x))/(x^8*log(x^2)^16+4*x^7*log(x^2)^12+(6*x^6-2*x^5+10*x^4)*log(x^2)^8+(4*x^5-4*x^4+20*x^3)*log(x^2)^4+x^4-2*x^3+11*x^2-10*x+25),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \frac {10 \, e^{\left (x + e^{x}\right )}}{x^{4} e^{x} \log \left (x^{2}\right )^{8} + 2 \, x^{3} e^{x} \log \left (x^{2}\right )^{4} + x^{2} e^{x} - x e^{x} + 5 \, e^{x}} \]

Giac 1.7.0 via sagemath 9.3 output

\[ \text {Timed out} \]________________________________________________________________________________________